#### Binomial Theorem, Sequences and Series One Mark Question

11th Standard

Reg.No. :
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Maths

Time : 00:30:00 Hrs
Total Marks : 10
10 x 1 = 10
1. If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

(a)

2

(b)

1

(c)

4

(d)

16

2. The HM of two positive numbers whose AM and GM are 16,8 respectively is

(a)

10

(b)

6

(c)

5

(d)

4

3. The nth term of the sequence 1, 2, 4, 7, 11,... is

(a)

n3+3n2+2n

(b)

n3-3n2+3n

(c)

$\frac { n(n+1)(n+2) }{ 3 }$

(d)

$\frac { { n }^{ 2 }-n+2 }{ 2 }$

4. The sum of an infinite GP is 18. If the first term is 6, the common ratio is

(a)

$\frac { 1 }{ 3 }$

(b)

$\frac { 2 }{ 3 }$

(c)

$\frac { 1 }{ 6 }$

(d)

$\frac { 3 }{ 4 }$

5. If the sum of n terms of an A. P. be 3n2 - n and its common difference is 6, then its first term is

(a)

2

(b)

3

(c)

1

(d)

4

6. The term without x in ${ \left( 2x-\frac { 1 }{ 2{ x }^{ 2 } } \right) }^{ 12 }$ is

(a)

495

(b)

-495

(c)

-7920

(d)

7920

7. The first and last term of an A.P.are 1 and 11.If the sum of its terms is 36, then the number of terms will be

(a)

5

(b)

6

(c)

7

(d)

8

8. If in an infinite G. P., first term is equal to 10 times the sum of all successive terms, then its common ratio is

(a)

$\frac { 1 }{ 10 }$

(b)

$\frac { 1 }{ 11 }$

(c)

$\frac { 1 }{ 9 }$

(d)

$\frac { 1 }{ 20 }$

9. The nth term of a G. Pis 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is

(a)

1

(b)

3

(c)

8

(d)

none of these

10. The value of ${ 9 }^{ \frac { 1 }{ 3 } }$ ,${ 9 }^{ \frac { 1 }{ 9 } }$${ 9 }^{ \frac { 1 }{ 27 } }$ ,$\infty$is

(a)

1

(b)

3

(c)

9

(d)

none of these